1. Technical Field of the Invention
The present invention relates in general to simplified whitening filtering in digital communications systems and, more particularly, to noise whitening filtering in communications systems operating according to Global System of Mobile communications (GSM).
2. History of Related Art
Receiver performance in wireless digital time-division multiple access (TDMA) communication systems such as, for example, those operating according to Global System for Mobile communications (GSM), Enhanced Data GSM Evolution (EGDE), and Digital Advanced Mobile Service (DAMPS), is often interference-limited. Interference might come from, for example, other users. Users operating on identical carrier frequencies in neighboring cells might create co-channel interference (CCI), while users operating on adjacent carrier frequencies might create adjacent-channel interference (ACI).
ACI is typically dominated by interference from first adjacent channels, since interference from secondary adjacent channels can be effectively suppressed by a receiver filter. CCI and ACI typically appear as colored noise. A receiver demodulator based on Maximum-Likelihood Sequence Estimation (MLSE) is optimal only in the presence of white noise. Therefore, if not compensated for, colored noise can significantly degrade performance of receiver equalizers based on MLSE.
There are two primary approaches to whitening colored noise: 1) implicit whitening; and 2) explicit whitening. The implicit-whitening approach incorporates a whitening function in a so-called pre-filter (i.e., a whitened matched filter) when an equalizer with decision feedback is employed. Decision feedback equalizer (DFE) and decision feedback sequence estimator (DFSE) are examples of decision feedback. The implicit-whitening approach requires a pre-filter having a length that is much longer than a span of a corresponding channel. An ideal pre-filter is anti-causal and unlimited in time and can only be approximated. In addition, setup and processing of the pre-filter is often computationally expensive because the pre-filter setup involves spectrum factorization of the propagation channel and inversing the maximum/phase factor of the channel.
FIG. 1 is a functional block diagram that illustrates an exemplary explicit-whitening process. In FIG. 1,  indicates a dependency relationship. Variables shown in FIG. 1 are as follows:
rreceived signalr′updated received signalttraining sequencepsynchronization positionh{n}n tap channel estimateh′{n+m}n + m tap updated channel estimateρnoise correlatew{m+1}whitening filter coefficientsssymbol estimate
An explicit-whitening process 100 begins with burst synchronization of the received signal r at a synchronization block 102. The received signal r is also input to a channel estimate block 104, a noise correlation block 106, and a whitening filter block 110. The synchronization block 102 outputs the synchronization position p to the channel estimate block 104. The n-tap channel estimate h{n} is calculated at the channel estimate block 104 and is output to the noise correlation block 106. Autocorrelation of noise samples is performed at the noise correlation block 106. The noise correlation block 106 outputs the noise correlate ρ to a whitening-filter-setting block 108. Whitening-filter settings determined by the whitening-filter-setting block 108 are input to a whitening-filter block 110.
The whitening-filter-setting block 108 may be adapted to solve a Yule-Walker equation using the noise correlate ρ. The output of the whitening filter block 110 is an updated received signal r′. The channel for the received signal r is n taps in length, while the composite channel for the updated received signal r′ is n+(m+1)−1=n+m taps in length. The updated received signal r′ output by the whitening filter block 110 is a convolution of the received signal r and the whitening filter of the whitening-filter block 110.
A second channel estimate is made at a channel estimate block 112. The second channel estimate, which is usually made via a generalized least square (GLS) algorithm, exploits knowledge of the whitening filter block 110. The second channel estimation is performed in order to obtain more accurate information about the composite channel to be input to an equalizer 114. The equalizer 114 receives as inputs an n+m tap updated channel estimate h′{n+m} from the channel estimate block 112 and the updated received signal r′ from the whitening-filter block 110. The equalizer 114 outputs the symbol estimate s.
The composite channel for the updated received signal r′ has a greater number of taps compared to the number of taps of the channel for the received signal r. The complexity of an MLSE equalizer (e.g., the equalizer 114) is determined by a composite-channel span. For binary modulations such as, for example, Gaussian minimum shift keying (GMSK) in GSM, an MLSE equalizer using a Viterbi algorithm has 2n−1 states, where n is the channel span. In order to implement the process 100, a full MLSE equalizer must therefore have 2n+m−1 states.
Even when the whitening filter block 110 is as short as a second order FIR filter, the equalizer 114 must still be four times more complex, due to the extension of the channel span. In addition, solving the Yule-Walker equation directly, with or without order recursion, is not always optimal in channel conditions with strong adjacent channel interference because the noise autocorrelation, and particularly elements at greater lags, are not accurate due to noise estimation error in strong ACI interferences.